fundiver made a good point- you will still get to see this dudes hand if you fold!
My own notes:
Pre: I don't hate playing 87o, but admittedly it is not the best, especially OOP. If it's suited, we could maybe incorporate it into our 3-bet range. We also need to account for what BB is playing here, when he calls and when he 3-bets. If you're calling with a lot of hands pre, expect BB to 3-bet squeeze some % of the time.
Flop: You are first to act with 2 players left, one being the initial raiser. Why bet here? They will fold their air and maybe get nervous with moderate holdings.
By checking, you let them bet their Ace highs (BB may do this), their pocket pairs that missed, and all their Qs. Depending on the strength of the bet you can just call or reraise.
Turn: This guy called your flop bet and BTN's over-bet shove, so he is strong. But since he is so strong you may just want to check to him and see what he does. Turn card didn't change anything. He may value bet KQ, maybe even AQ, maybe he is getting tricky with KK or AA if he is that type of player.
There are certainly more hands that you beat than those that beat you, but it's hard to think about a pair of queens ripping it (nearly) all-in here. Once you see the raise you can guess this guy has a boat.
A7 would be more of a hand I assign to BTN
__________________
|